Results 51 to 60 of about 750 (182)

Riemann–Liouville Type Fractional Derivatives and Equivalences of Linear Riemann–Liouville Type Fractional Differential Equations

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT The first or higher order Riemann–Liouville (R‐L) type fractional derivatives are studied. The relations between the R‐L type fractional derivatives and the classical R‐L fractional derivatives are obtained and the spaces of functions on which the R‐L type fractional derivatives exist are provided.
Kunquan Lan
wiley   +1 more source

On multiplicative conformable fractional integrals: theory and applications

Boundary Value Problems
In this paper, we first introduce the multiplicative conformable left and right fractional integrals, followed by the derivation of key properties, such as integrability, boundedness, continuity, and the semi-group property, for the newly defined ...
Hüseyin Budak, Büşra Betül Ergün
doaj   +1 more source

Fractional Probability Theory of Arbitrary Order

Fractal and Fractional, 2023
A generalization of probability theory is proposed by using the Riemann–Liouville fractional integrals and the Caputo and Riemann–Liouville fractional derivatives of arbitrary (non-integer and integer) orders. The definition of the fractional probability
Vasily E. Tarasov
doaj   +1 more source

Sliding Mode Control in Aerospace Applications: A Survey

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT Sliding mode control (SMC) enjoys robustness to matched and unmatched (in the case of minimum phase input‐output dynamics) bounded perturbations, and finite time convergence. Second‐order and higher‐order sliding mode control systems (2‐SMC/HOSMC) retain all the advantages of sliding mode control, but in addition can be applied to systems of ...
Yuri Shtessel, Christopher Edwards
wiley   +1 more source

Generalized Fractional Integral Inequalities of σ-Convex Functions

Journal of Mathematics
In this paper, we prove generalized fractional integral inequalities of Hermite–Hadamard–type with respect to a monotone function for σ-convex functions on account of the Riemann–Liouville fractional integral.
Shweta Lather, Harish Nagar
doaj   +1 more source

A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative

Mathematics, 2019
New versions of a Gronwall−Bellman inequality in the frame of the generalized (Riemann−Liouville and Caputo) proportional fractional derivative are provided.
Jehad Alzabut, Weerawat Sudsutad, Zeynep Kayar, Hamid Baghani   +3 more
doaj   +1 more source

On Multiple Positive Solutions for Singular Fractional Boundary Value Problems with Riemann-Stieltjes Integrals

Journal of Function Spaces, 2023
In this paper, the existence result of at least two positive solutions is obtained for a nonlinear Riemann-Liouville fractional differential equation subject to nonlocal boundary conditions, where fractional derivatives and Riemann-Stieltjes integrals ...
Lufeng Gu, Qiuyan Zhong, Zhuyan Shao
doaj   +1 more source

Fractional Integral Inequalities of Riemann–Liouville Type for Higher‐Order Differentiable Convex Mappings

Mathematical Methods in the Applied Sciences, Volume 49, Issue 11, Page 12313-12323, 30 July 2026.
ABSTRACT In this paper, we investigate several Riemann–Liouville fractional integral inequalities for higher‐order differentiable functions using a simple and novel approach. First, we present an inequality involving fractional integrals that generalizes the right‐hand side of the fundamental Hermite–Hadamard inequality to higher‐order derivatives ...
Samet Erden, Hüseyin Budak
wiley   +1 more source

Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,qx$$ {M}_n^{\left(p,q\right)}(x) $$

Mathematical Methods in the Applied Sciences, Volume 49, Issue 11, Page 12524-12538, 30 July 2026.
ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature.
Esra Güldoğan Lekesiz
wiley   +1 more source

On an Inequality of H. G. Hardy

Journal of Inequalities and Applications, 2010
We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville type ...
Krulić Kristina, Iqbal Sajid, Pečarić Josip   +2 more
doaj